Cryptology ePrint Archive: Report 2006/162

A Summary of McEliece-Type Cryptosystems and their Security

D. Engelbert, R. Overbeck and A. Schmidt

Abstract: In this paper we give an overview of some of the cryptographic
applications which were derived from the proposal of R.J. McEliece to
use error correcting codes for cryptographic purposes.
Code based cryptography is an interesting alternative to number theoretic cryptography. Many basic cryptographic functions like encryption, signing, hashing, etc. can be
realized using code theoretic concepts.

In this paper we briefly show how to correct errors in transmitted data by employing Goppa codes and describe possible applications to public key cryptography.

The main focus of this paper is to provide detailed insight
into the state of art of cryptanalysis of the McEliece
cryptosystem and the effect on different cryptographic applications.
We conclude, that for code based cryptography a public key of $88$KB
offers sufficient security for encryption, while we need a public key
of at least $597$KB for secure signing.